A native of Nelson, British Columbia, Greg Adams played his junior hockey with the Kelowna Buckaroos of the BCJHL. At the age of 20 he enrolled at the University of Northern Arizona, deciding it would be prudent to achieve an education. During his two seasons at the school, Adams became one of the top offensive performers in the ACHA. NHL scouts took note of Adams's scoring prowess, especially during the 1983-84 campaign, when he netted 44 goals and 73 points in just 26 games.
In the summer of 1984, the New Jersey Devils, who offered him a free-agent contract, approached Adams. During his first year as a pro, Adams spent half the season with the Devils and the other half in the minors with the Maine Mariners where he developed into a stronger two-way player. In 1985-86 Adams won a spot on the Devils roster and in his first full season in the NHL responded with 35 goals and 77 points.
After another season in New Jersey, Adams was traded to the Vancouver Canucks along with goalie Kirk McLean. It was in Vancouver that Adams spent the bulk of his NHL career and is also where he enjoyed most of his personal successes. In over seven seasons with the Canucks, Adams was often relied upon to spearhead the offensive charge along with the likes of Pavel Bure and Trevor Linden. Adams was a homegrown boy from Nelson. "In my first game with Vancouver, we played the St. Louis Blues," Adams recalled. "I scored four goals." He potted a career-high 36 goals in 1987-88, when he played in all 80 Canuck games, which was a rarity throughout his career, suffering from an assortment of nagging injuries, which often kept him on the sidelines.
The highlight of Adams's career came in 1994, when the Canucks came within one game of winning the Stanley Cup, only to lose the deciding seventh game to the New York Rangers. Adams is perhaps best remembered for his two clutch playoff goals that postseason. The first was against the Toronto Maple Leafs in Game Five of the 1994 Conference Finals, the overtime winning goal to complete a comeback from three goals down. The goal sent the Canucks to the Stanley Cup Finals. Adams then managed to top that when he scored the winning goal in Game One of the finals against the Rangers, but in the end they came up one victory short of the title.
Adams spent three years with the Dallas Stars, but once again found himself on the sidelines when the injury bug hit on more than one occasion. The Stars traded Adams to the Los Angeles Kings at the 1995 NHL Entry Draft, although he never actually played for them. Wanting to prove he could still play in the NHL, Adams signed a free-agent contract with the Phoenix Coyotes in 1998, and he responded with two consecutive 40-plus point seasons. Adams suited up for his 17th and final season in 2000-01 with the Florida Panthers.
After being away from the game for a year, Adams suited up for the Frankfurt Lions in 2002-03 before calling it a career for good after the season.